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An investor with assets of 10,000 has an opportunity to invest 5000 in a venture that is equally likely to pay either 15,000 or nothing. The investors utility function can be described by the log utility function U(x)=ln(x), where x is his total wealth.
a) What should the investor due?
b) Suppose the investor places a bet with a friend before making the investment decision. The bet is for 1000; if a fair coin lands heads up, the investor wins 1000, but if it lands tails up, the investor pays 1000 to his friend. Only after the bet has been resolved will the investor decide whether or not to invest in the venture. What is an appropriate strategy for the investor? If he wins the bet, should he invest? What if he loses the bet?
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